Generation of Random Orthogonal Matrices

Abstract

In order to generate a random orthogonal matrix distributed according to Haar measure over the orthogonal group it is natural to start with a matrix of normal random variables and then factor it by the singular value decomposition. A more efficient method is obtained by using Householder transformations. We propose another alternative based on the product of ${{n(n - 1)}/2}$ orthogonal matrices, each of which represents an angle of rotation. Some numerical comparisons of alternative methods are made.